Related papers: Ap\'ery-like numbers for non-commutative harmonic …

In this paper, motivated by studying special values of zeta functions attached to finite type F_p-schemes, we introduce a category of ``arithmetic C(S^1,R)-modules'' attached to any Dedekind ring R, and compute the 0th K-group of this…

We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary. The eigenvalues of the principal symbol are assumed to be…

We introduce a vector-valued generalization of the Epstein zeta functions associated with the root lattices of ADE-type Lie algebras. The quadratic forms defining these lattices correspond to the Gram matrices of the simple roots. Using the…

By applying p-adic integral on the set of p-adic integers in [27] (Interpolation Functions for New Classes Special Numbers and Polynomials via Applications of p-adic Integrals and Derivative Operator, Montes Taurus J. Pure Appl. Math. 3…

Recently, Mertens, Ono, and the third author studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a…

We investigate integrality and divisibility properties of Fourier coefficients of meromorphic modular forms of weight $2k$ associated to positive definite integral binary quadratic forms. For example, we show that if there are no…

We classify all invariants of the functor $I^n$ (powers of the fundamental ideal of the Witt ring) with values in $A$, that it to say functions $I^n(K)\rightarrow A(K)$ compatible with field extensions, in the cases where $A(K)=W(K)$ is the…

Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of…

This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel…

Let $p$ and $q$ be distinct prime numbers, with $q\equiv 1\pmod{12}$. Let $N$ be a positive integer that is coprime to $pq$. We prove a formula relating the Hasse--Weil zeta function of the modular curve $X_0(qN)_{\mathbb{F}_q}$ to the…

We consider the one-parameter generalization $S^4_q$ of 4-sphere with a conical singularity due to identification $\tau=\tau + 2 \pi q$ in one isometric angle. We compute the value of the spectral zeta-function at zero $z(q) = \zeta(0, q)$…

We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In the case of singular weight, we show that the orthogonal non-holomorphic Eisenstein series that can be written as…

We study the statistics of scalar perturbations in models of inflation with small and rapid oscillations in the inflaton potential (resonant non-Gaussianity). We do so by deriving the wavefunction $\Psi[\zeta(\boldsymbol{x})]$…

Using the FiNLIE solution of the AdS/CFT Y-system, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a non reducible Euler-Zagier sum,…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

By using the Wilf-Zeilberger method, we prove a novel finite combinatorial identity related to a bivariate generating function for $\zeta(2+r+2s)$ (an extension of a Bailey-Borwein-Bradley Apery-like formula for even zeta values). Such…

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…

In this paper, we investigate the non-modular solutions to the Schwarz differential equation $\{f,\tau \}=sE_4(\tau)$ where $E_4(\tau)$ is the weight 4 Eisenstein series and $s$ is a complex parameter. In particular, we provide explicit…

In this paper we find some exponential formulas for the Betti numbers of the De Concini-Procesi minimal wonderful models Y_{G(r,p,n)} associated to the complex reflection groups G(r,p,n). Our formulas are different from the ones already…

Our previous work dealt with the zeta function for the interacting particle system (IPS) including quantum cellular automaton (QCA) as a typical model in the study of ``IPS/Zeta Correspondence". On the other hand, the absolute zeta function…